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Rahmat (62), Shahidi (58 not out), who completed 2000 ODI runs, and Omarzai (73 not out) led the chase with aplomb as Afghanistan overhauled the target of 242 in just 45.2 overs.
Earlier, Sri Lanka produced a dull batting effort to get bundled out for 241.
They were rocked by pacer Fazalhaq Farooqi who grabbed four wickets conceding just 34 runs in his quota of 10 overs.
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Sri Lanka: 241 all out in 49.3 overs (Pathum Nissanka 46; Fazalhaq Farooqi 4/34)Afghanistan: 242 for 3 in 45.2 overs (Rahmat Shah 62, Hashmatullah Shahidi 58 not out, Azmat Omarzai 73 not out) by 7 wickets.